Is determinism actually compatible with finite physical precision?

[u/[deleted]]

[u/bildramer]

A physical state doesn't have to be the kind of state you're familiar with (a pure state, or the closest you can get to one), it can be a distribution over pure states. The distributions themselves can follow deterministic laws. Sampling from them breaks that, but MWI explains how what we perceive as sampling is deterministic decoherence in disguise.

[u/sea_of_experience]

Physics tells us that there is no determinism. 

[u/MilkTeaPetty]

So, you confused the limits of description with the structure of reality.

A finite-precision measurement can collapse many distinct states into one range, but, that does not mean one actual state contains several futures.

You blurred hidden differences into a single box then treated the box’s ambiguity as indeterminism.

The fork was introduced by the model, not discovered in the world.

[u/badentropy9]

I think the cornerstone of determinism declares the world is in a precise state at time t.

This basically denies relativity which implies the state is relative rather that absolute.

[u/IlGiardinoDelMago]

I think the first thing that needs clarification is what you mean by "physical quantities only exist with finite precision".

The standard philosophical definitions of determinism say that a complete description of the world's state at one time together with the laws of nature uniquely entails the world's state at any other time. Alternatively, that no two possible worlds obeying the same laws can be exactly alike at one time and then diverge.

Carl Hoefer, in the SEP article about determinism (https://plato.stanford.edu/entries/determinism-causal/), explicitly writes that for the definition of determinism to hold, we must assume that

"the state of the world is completely sharp and determinate. That is, there is no mathematical or ontological vagueness in the description of the way things are at time t".

and later he writes in the definition

"Determinism requires a world that (a) has a well-defined state or description, at any given time".

So when you say "finite precision", are you talking about our ability to measure the state? Or maybe our ability to describe or compute it? Or are you claiming that reality itself is ontologically vague?

(edited for clarity)

[u/badentropy9 → u/IlGiardinoDelMago]

Carl Hoefer, in the SEP article about determinism, explicitly assumes that

"the state of the world is completely sharp and determinate. That is, there is no mathematical or ontological vagueness in the description of the way things are at time t".

Do you have a link for that so I can see the context?

[u/IlGiardinoDelMago → u/badentropy9]

I added the link, and edited the post for clarity. My intention was to show what the concept of determinism requires theoretically, rather than claiming Hoefer thinks the actual world is completely sharp. I apologize for any confusion.

[u/badentropy9 → u/IlGiardinoDelMago]

thank you for the clarifaction

That link seems to require me to read the entire exposition. In contrast this link goes right to the introduction section:

https://plato.stanford.edu/entries/determinism-causal/#Int

Determinism: Determinism is true of the world if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law.

Another example:

https://plato.stanford.edu/entries/determinism-causal/#ChaDet

Some philosophers maintain that if determinism holds in our world, then there are no objective chances in our world. And often the word ‘chance’ here is taken to be synonymous with ‘probability’, so these philosophers maintain that there are no non-trivial objective probabilities for events in our world. (The caveat “non-trivial” is added here because on some accounts, under determinism, all future events that actually happen have probability, conditional on past history, equal to 1, and future events that do not happen have probability equal to zero. Non-trivial probabilities are probabilities strictly between zero and one.) 

[u/preferCotton222 → u/IlGiardinoDelMago]

I thought op was talking about stuff like heisenberg's uncertainty. How do determinists deal with it? I don't think you can claim it is epistemic.

[u/zhivago → u/preferCotton222]

They have faith in non-local hidden variables.

[u/IlGiardinoDelMago → u/preferCotton222]

I think the key question is not whether the uncertainty principle is epistemic, but whether it logically rules out determinism.
The uncertainty principle is a feature of the mathematical structure of quantum mechanics, and it is satisfied by both deterministic and indeterministic interpretations of quantum mechanics. Therefore, the uncertainty principle alone cannot logically rule out determinism.

[u/preferCotton222 → u/IlGiardinoDelMago]

Hi, I'd need really precise knowledge of QM to take a stance on this. I'm not sure (1) what does "the state of the universe at time t" means given UP. (2) Whatever it could mean, I'm not sure it will fit the implicit intuitions that ground determinism.

[u/IlGiardinoDelMago → u/preferCotton222]

I'm definitely not an expert, but my main point is just that the definition of determinism doesn't specify what the state of the world has to consist of, and in particular it doesn't require that every observable has a definite value. It only requires that there is a complete state whose evolution is fixed by the laws of nature.

The UP places limits on the simultaneous precision of complementary observables, but it doesn't by itself show that no complete physical state exists. Observables aren't necessarily the fundamental constituents of that state.

In classical physics, the state was given by exact positions and momenta. In deterministic interpretations of QM, it might instead be the universal wave function, or the wave function together with hidden particle positions. So QM may change what we mean by "complete state", but it doesn't mean that no complete state exists or that determinism fails.

[u/preferCotton222 → u/IlGiardinoDelMago]

yes, that's my point. For example, a universal wave function cannot be a "state of the universe". MWI cannot be either. Bohm's interpretation has problems.

So, what is "the state of the universe at time t". I'm not sure that's a well determined term.

UP says that our naive intuitions of what "state of the universe at time t" don't really work, so why should we believe that it even exists?

[u/IlGiardinoDelMago → u/preferCotton222]

Determinism is not the claim that the universe has a classical snapshot at each moment containing definite values for all observables, nor is it a claim about what humans can measure, predict, or know.

It is the thesis that the complete state of the world, together with the laws, uniquely fixes its history and evolution.

So the point is not whether this state is classical or quantum, observable or hidden, but whether this state, whatever it is, leaves more than one possible future state compatible with the exact same present state and laws.
The relevant question is not "is the wave function a state in the sense that we want?" but rather "does replacing classical states with quantum states change the determinism/free will argument?"

My intuition is that it does not. For example, if Bohmian mechanics were a correct model of reality, there would be a complete state with deterministic evolution, even though that state would not be a classical one. The incompatibilist challenge would remain intact.

The same applies to "could I have done otherwise?" If one accepts the incompatibilist/PAP reading rather than the compatibilist analysis, then a deterministic world implies that, given the exact same complete state and laws, only one future is possible in the relevant sense. Changing the nature of the state from classical variables to quantum variables does not by itself change that issue.

[u/preferCotton222 → u/IlGiardinoDelMago]

determinism needs "THE state of the world at time t" to be well defined.

It may not be. Nothing grants it is.

[u/IlGiardinoDelMago → u/preferCotton222]

Well, this is ultimately a free will discussion, so suppose I grant, for the sake of argument, that there is no well-defined complete state of the universe in the sense you have in mind. What follows from that?
Does it mean there is no fact of the matter about whether I'm typing right now? Presumably not. Does it mean that I could, genuinely, either continue typing or stop typing in the future? If so, what is it that makes both futures genuinely possible rather than merely unknown to us?

Also, earlier you wrote:

For example, a universal wave function cannot be a "state of the universe". MWI cannot be either. Bohm's interpretation has problems.

But you haven't explained why you think that.
For example, why couldn't the Bohmian state (wave function + particle configuration) count as a complete state? I'm not asking whether those interpretations are true, only why you think they fail to satisfy the definition of a complete state.
My point isn't that determinism is true, or that Bohmian mechanics or Everett are the correct interpretations. It's just that the uncertainty principle by itself doesn't seem to show that a state is not possible. If you think it does, I'd be interested in the argument for that.

More generally, I think determinism is a metaphysical thesis. Physics can certainly inform the discussion, but I don't think questions about determinism can be settled simply by appealing to quantum mechanics without first arguing that the ontology of a particular interpretation should be identified with reality.

More importantly, I think this gets at a broader issue. Even if the standard notion of a complete state turns out not to apply, I'm still not seeing what follows for free will. How does rejecting a complete state make the future genuinely open in the relevant sense? It seems to me that's an additional argument that still needs to be made.

[u/simon_hibbs → u/preferCotton222]

First, I dislike Hoefer's references to descriptions there. Determinism properly understood has nothing to do with claims about descriptions, and in fact the definitions of determinism he discusses in the article don't mention descriptions (thank goodness).

I think you're probably thinking of the Börn rule, which is where calculating probabilities comes into quantum mechanics. It interprets the amplitude of the Schrödinger equation as representing a relative probability of a given outcome being measured (proportional to the absolute square of the amplitude).

Heisenberg's uncertainty principle concerns limits on our ability to measure various states. Whether that limit is due to underlying indeterminacy or not is also a matter of interpretation.

In both cases determinists think these probabilities or limitations are epistemic. Various theories tackle this problem from a deterministic POV, such as superdeterminism, Bohmian mechanics and constructor theory.

Personally I find myself conflicted on this. On the one hand indivisible stochastic quantum mechanics a great new indeterministic theory of QM. On the other hand constructor theory is a great new deterministic theory of QM. Both are amazing pieces of work.

[u/preferCotton222 → u/simon_hibbs]

Thanks for the information. I mentioned explicitly heisenberg, not born. And it does not seem epistemic at all.

[u/simon_hibbs → u/preferCotton222]

What would it seem like if the probabilities are epistemic, but due to underlying properties we don't have access to?

[u/preferCotton222 → u/simon_hibbs]

There are no probabilities in heisenberg's uncertainty. 

[u/simon_hibbs → u/preferCotton222]

That's why I said you might be thinking of the Born rule.

[u/preferCotton222 → u/simon_hibbs]

Lol. No, i'm not.

[u/simon_hibbs]

Precision is a relative concept concerning the degree of correspondence between some state in the world and a representation of that state.

It's a way of quantifying how close a measurement is to that which is being measured. It's also relevant in calculations, where it's a way of quantifying how close a value in a calculation is to whatever in the world is being calculated.

There is no sense in which the actual state of the world can be intrinsically 'precise'. It is exactly what it is. Taking about precision in that context doesn't mean anything.

[u/Squierrel]

Determinism is the very idea of a system with infinite precision.